Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions

Abstract

Abstract The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized $$(\psi ,\phi )$$ ( ψ , ϕ ) -contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of $$(\psi ,\phi )$$ ( ψ , ϕ ) . Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of $$\psi$$ ψ and $$\phi$$ ϕ and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

Keywords

• Fixed point
• Integral inclusion
• Integral equations
• RLC-circuits
• Fractal fractional differential equations
• Extended b-metric space